Question

If one angle of a triangle is 45° and the other two angles are in the ratio 1:2, find
these angles​

Answer 1

Answer:

angle 2 = 45°, angle 3 = 90°

Step-by-step explanation:

Sum of all interior angles of a triangle = 180°

angle 1 = 45 °

therefore, sum of angles 2 and 3 = 180° - 45° = 135°

ratio of other angles -> 1 : 2

therefore 135° has to be divided into three (1+2)

135/3 = 45°

1 : 2

1 (45) : 2 (45)

45 : 90

therefore,

angle 2 = 45°, angle 3 = 90°

Answer 2

Answer:

45°, 90°

Step-by-step explanation:

If we take ∠A,∠B and ∠C as the 3 angles of a triangle,

here we are given with ∠A=45°

also, we know that ∠A + ∠B + ∠C = 180°

=> 45° + ∠B + ∠C = 180°

=> ∠B + ∠C = 180°-45°

=> ∠B + ∠C = 135° -------- (1)

Given that ∠B : ∠C = 1:2

if x be the proportional constant,

then we have  (1) = x + 2x = 135°

=> 3x = 135°

=> x = 135/3 = 45°

hence the other angles are x, 2x

ie., 45°, 2(45°)

ie., 45°, 90°